Update by Ali

[ThesisAli.git] / CHAPITRE_05.tex

diff --git a/CHAPITRE_05.tex b/CHAPITRE_05.tex
index 9afbba18901e288537df7df3d84af65aab97df55..ba1dc5abfd5748ff207a1089af769820e2096dee 100755 (executable)
--- a/CHAPITRE_05.tex
+++ b/CHAPITRE_05.tex
@@ -7,6 +7,8 @@
 \chapter{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
 \label{ch5}
 
 \chapter{Multiround Distributed Lifetime Coverage Optimization Protocol in Wireless Sensor Networks}
 \label{ch5}
 

+\iffalse
+

 \section{Summary}
 \label{ch5:sec:01}
 Coverage and lifetime are two paramount problems in Wireless  Sensor Networks (WSNs). In this paper, a method called Multiround Distributed Lifetime Coverage
 \section{Summary}
 \label{ch5:sec:01}
 Coverage and lifetime are two paramount problems in Wireless  Sensor Networks (WSNs). In this paper, a method called Multiround Distributed Lifetime Coverage


@@ -17,6 +19,47 @@ lifetime of  WSN. The decision process is  carried out by a  leader node, which
 during the rounds  of the sensing phase. Compared  with some existing protocols, simulation  results based  on  multiple criteria  (energy consumption,  coverage
 ratio, and  so on) show that  the proposed protocol can  prolong efficiently the network lifetime and improve the coverage performance.
 
 during the rounds  of the sensing phase. Compared  with some existing protocols, simulation  results based  on  multiple criteria  (energy consumption,  coverage
 ratio, and  so on) show that  the proposed protocol can  prolong efficiently the network lifetime and improve the coverage performance.
 

+\fi
+
+\section{Introduction}
+\label{ch5:sec:01}
+
+\indent  The fast  developments of low-cost  sensor devices  and  wireless
+communications have allowed the emergence of WSNs. A WSN includes a large number
+of small, limited-power sensors that  can sense, process, and transmit data over
+a wireless  communication. They communicate  with each other by using multi-hop
+wireless communications and cooperate together  to monitor the area of interest,
+so that  each measured data can be  reported to a monitoring  center called sink
+for further  analysis~\cite{ref222}.  There  are several fields  of application
+covering  a wide  spectrum for a  WSN, including health, home, environmental,
+military, and industrial applications~\cite{ref19}.
+
+On the one hand sensor nodes run on batteries with limited capacities, and it is
+often  costly  or  simply  impossible  to  replace  and/or  recharge  batteries,
+especially in remote and hostile environments. Obviously, to achieve a long life
+of the  network it is important  to conserve battery  power. Therefore, lifetime
+optimization is one of the most critical issues in wireless sensor networks. On
+the other hand we must guarantee  coverage over the area of interest. To fulfill
+these two objectives, the main idea  is to take advantage of overlapping sensing
+regions to turn-off redundant sensor nodes  and thus save energy. In this paper,
+we concentrate  on the area coverage  problem, with the  objective of maximizing
+the network lifetime by using an optimized multiround scheduling.
+
+We study the problem of designing an energy-efficient optimization algorithm that divides the sensors in a WSN into multiple cover sets such that the area of interest is monitored as long as possible. Providing multiple cover sets can be used to improve the energy efficiency of WSNs. Therefore, in order to increase the longevity of the WSN and conserve the energy, it can be useful to provide multiple cover sets in one time after that schedule them for multiple rounds, so that the battery life of a sensor is not wasted due to the repeated execution of the coverage optimization algorithm, as well as the information exchange and leader election.
+
+The MuDiLCO protocol (for Multiround Distributed Lifetime Coverage Optimization protocol) presented in this chapter is an extension of the approach introduced in chapter 4. Simulation results have shown that it was more interesting to divide the area into several subregions, given the computation complexity. Compared to our protocol in chapter 4, in this one we study the possibility of dividing the sensing phase into multiple rounds. In fact, in this chapter we make a multiround optimization, while it was a single round optimization in our protocol in chapter 4.
+
+The remainder of the chapter continues with section \ref{ch5:sec:02} where a detail of MuDiLCO Protocol is presented. The next section describes the Primary Points based Multiround Coverage Problem formulation  which is used to schedule the activation of sensors in T cover sets. Section \ref{ch5:sec:04} shows the simulation
+results. The chapter ends with a conclusion and some suggestions for further work.
+
+
+ 
+
+
+
+
+
+

 \section{MuDiLCO Protocol Description}
 \label{ch5:sec:02}
 \noindent In this section, we introduce the MuDiLCO protocol which is distributed on each subregion in the area of interest. It is based on two energy-efficient
 \section{MuDiLCO Protocol Description}
 \label{ch5:sec:02}
 \noindent In this section, we introduce the MuDiLCO protocol which is distributed on each subregion in the area of interest. It is based on two energy-efficient


@@ -39,7 +82,7 @@ task. Each sensor node in the subregion will
 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
 sleep for  each round of the sensing  phase.  Algorithm~\ref{alg:MuDiLCO}, which
 will be  executed by each node  at the beginning  of a period, explains  how the
 receive an Active-Sleep packet from WSNL, informing it to stay awake or to go to
 sleep for  each round of the sensing  phase.  Algorithm~\ref{alg:MuDiLCO}, which
 will be  executed by each node  at the beginning  of a period, explains  how the

-Active-Sleep packet is obtained. In this way a multiround optimization  process is performed  during each
+Active-Sleep packet is obtained. In this way, a multiround optimization  process is performed  during each

 period  after  Information~Exchange  and  Leader~Election phases,  in  order  to
 produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
 \begin{figure}[ht!]
 period  after  Information~Exchange  and  Leader~Election phases,  in  order  to
 produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
 \begin{figure}[ht!]


@@ -51,9 +94,9 @@ produce $T$ cover sets that will take the mission of sensing for $T$ rounds.
 
 This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods. 
 
 
 This protocol minimizes the impact of unexpected node failure (not due to batteries running out of energy), because it works in periods. 
 

-On the one hand, if a node failure is detected before making the decision, the node will not participate to this phase, and, on the other hand, if the node failure occurs after the decision, the sensing  task of the network will be temporarily affected:  only during  the period of sensing until a new period starts.
+On the one hand, if a node failure is detected before making the decision, the node will not participate during this phase, and, on the other hand, if the node failure occurs after the decision, the sensing  task of the network will be temporarily affected:  only during  the period of sensing until a new period starts.

 
 

-The  energy consumption  and some  other constraints  can easily  be  taken into account,  since the  sensors  can  update and  then  exchange their  information (including their residual energy) at the beginning of each period.  However, the pre-sensing  phases (Information  Exchange, Leader  Election, and  Decision) are energy  consuming for some  nodes, even  when they  do not  join the  network to monitor the area.
+The  energy consumption  and some other constraints  can easily  be  taken into account since the  sensors  can  update and  then  exchange their  information (including their residual energy) at the beginning of each period.  However, the pre-sensing  phases (Information  Exchange, Leader  Election, and  Decision) are energy  consuming for some  nodes, even  when they  do not  join the  network to monitor the area.

 
  
 
 
  
 


@@ -100,8 +143,9 @@ The  energy consumption  and some  other constraints  can easily  be  taken into
 
 
 
 
 
 

-\subsection{Primary Points based Multiround Coverage Problem Formulation}
-%\label{ch5:sec:02:02}
+\section{Primary Points based Multiround Coverage Problem Formulation}
+\label{ch5:sec:03}
+

 
 According to our algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model
 proposed by  \cite{ref156} with some modifications, where  the objective is
 
 According to our algorithm~\ref{alg:MuDiLCO}, the integer program is based on the model
 proposed by  \cite{ref156} with some modifications, where  the objective is


@@ -117,7 +161,7 @@ involved in the integer program.
 
 
 For a  primary point  $p$, let $\alpha_{j,p}$  denote the indicator  function of
 
 
 For a  primary point  $p$, let $\alpha_{j,p}$  denote the indicator  function of

-whether the point $p$ is covered, that is:
+whether the point $p$ is covered, that is

 \begin{equation}
 \alpha_{j,p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 \alpha_{j,p} = \left \{ 
 \begin{array}{l l}


@@ -128,7 +172,7 @@ whether the point $p$ is covered, that is:
 %\label{eq12} 
 \end{equation}
 The number of  active sensors that cover the  primary point $p$ during
 %\label{eq12} 
 \end{equation}
 The number of  active sensors that cover the  primary point $p$ during

-round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where:
+round $t$ is equal to $\sum_{j \in J} \alpha_{j,p} * X_{t,j}$ where

 \begin{equation}
 X_{t,j} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 X_{t,j} = \left \{ 
 \begin{array}{l l}


@@ -137,7 +181,7 @@ X_{t,j} = \left \{
 \end{array} \right.
 %\label{eq11} 
 \end{equation}
 \end{array} \right.
 %\label{eq11} 
 \end{equation}

-We define the Overcoverage variable $\Theta_{t,p}$ as:
+We define the Overcoverage variable $\Theta_{t,p}$ as

 \begin{equation}
  \Theta_{t,p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
  \Theta_{t,p} = \left \{ 
 \begin{array}{l l}


@@ -150,7 +194,7 @@ We define the Overcoverage variable $\Theta_{t,p}$ as:
 More  precisely, $\Theta_{t,p}$  represents the  number of  active  sensor nodes
 minus  one  that  cover  the  primary  point $p$  during  round  $t$.   The
 Undercoverage variable  $U_{t,p}$ of the primary  point $p$ during  round $t$ is
 More  precisely, $\Theta_{t,p}$  represents the  number of  active  sensor nodes
 minus  one  that  cover  the  primary  point $p$  during  round  $t$.   The
 Undercoverage variable  $U_{t,p}$ of the primary  point $p$ during  round $t$ is

-defined by:
+defined by

 \begin{equation}
 U_{t,p} = \left \{ 
 \begin{array}{l l}
 \begin{equation}
 U_{t,p} = \left \{ 
 \begin{array}{l l}


@@ -160,7 +204,7 @@ U_{t,p} = \left \{
 \label{eq14} 
 \end{equation}
 
 \label{eq14} 
 \end{equation}
 

-Our coverage optimization problem can then be formulated as follows:
+Our coverage optimization problem can then be formulated as follows

 \begin{equation}
  \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p}  \right)  \label{eq15} 
 \end{equation}
 \begin{equation}
  \min \sum_{t=1}^{T} \sum_{p=1}^{P} \left(W_{\theta}* \Theta_{t,p} + W_{U} * U_{t,p}  \right)  \label{eq15} 
 \end{equation}


@@ -213,7 +257,7 @@ absence  of  monitoring  on  some  parts  of the  subregion  by  minimizing  the
 undercoverage.  The weights  $W_\theta$ and $W_U$ must be  properly chosen so as
 to guarantee that the maximum number of points are covered during each round. 
 %% MS W_theta is smaller than W_u => problem with the following sentence
 undercoverage.  The weights  $W_\theta$ and $W_U$ must be  properly chosen so as
 to guarantee that the maximum number of points are covered during each round. 
 %% MS W_theta is smaller than W_u => problem with the following sentence

-In our simulations priority is given  to the coverage by choosing $W_{U}$ very
+In our simulations, priority is given  to the coverage by choosing $W_{U}$ very

 large compared to $W_{\theta}$.
 
 
 large compared to $W_{\theta}$.
 
 


@@ -221,10 +265,10 @@ large compared to $W_{\theta}$.
  
 
 \section{Experimental Study and Analysis}
  
 
 \section{Experimental Study and Analysis}

-\label{ch5:sec:03}
+\label{ch5:sec:04}

 
 \subsection{Simulation Setup}
 
 \subsection{Simulation Setup}

-\label{ch5:sec:03:01}
+\label{ch5:sec:04:01}

 We  conducted  a  series of  simulations  to  evaluate  the efficiency  and  the
 relevance  of our  approach,  using  the  discrete   event  simulator  OMNeT++
 \cite{ref158}. The simulation  parameters are summarized in Table~\ref{table3}.  Each experiment  for  a network  is  run over  25~different random topologies and  the results presented hereafter are  the average of these
 We  conducted  a  series of  simulations  to  evaluate  the efficiency  and  the
 relevance  of our  approach,  using  the  discrete   event  simulator  OMNeT++
 \cite{ref158}. The simulation  parameters are summarized in Table~\ref{table3}.  Each experiment  for  a network  is  run over  25~different random topologies and  the results presented hereafter are  the average of these


@@ -276,17 +320,11 @@ $W_{U}$ & $|P|^2$
 % is used to refer this table in the text
 \end{table}
   
 % is used to refer this table in the text
 \end{table}
   

-Our protocol  is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5,
-and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of
-rounds in one sensing period).  In  the following, we will make comparisons with
-two other methods. The first method, called DESK and proposed by \cite{DESK},
-is  a   full  distributed  coverage   algorithm.   The  second   method,  called
+Our protocol  is declined into  four versions: MuDiLCO-1,  MuDiLCO-3, MuDiLCO-5, and  MuDiLCO-7, corresponding  respectively to  $T=1,3,5,7$ ($T$  the  number of rounds in one sensing period).  In  the following, we will make comparisons with two other methods. The first method, called DESK and proposed by \cite{DESK}, is  a   fully  distributed  coverage   algorithm.   The  second   method is called

 GAF~\cite{GAF}, consists in dividing  the region into fixed squares.
 GAF~\cite{GAF}, consists in dividing  the region into fixed squares.

-During the decision  phase, in each square, one sensor is  then chosen to remain
-active during the sensing phase time.
+During the decision  phase, in each square, one sensor is  then chosen to remain active during the sensing phase time.

 
 

-Some preliminary experiments were performed in chapter 4 to study the choice of the number of
-subregions  which subdivides  the  sensing field,  considering different  network
+Some preliminary experiments were performed in chapter 4 to study the choice of the number of subregions  which subdivides  the  sensing field,  considering different  network

 sizes. They show that as the number of subregions increases, so does the network
 lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
 network  disconnection due  to node  failures.  However,  too  many subdivisions
 sizes. They show that as the number of subregions increases, so does the network
 lifetime. Moreover,  it makes  the MuDiLCO protocol  more robust  against random
 network  disconnection due  to node  failures.  However,  too  many subdivisions


@@ -299,7 +337,7 @@ We used the modeling language and the optimization solver which are mentioned in
 %The initial energy of each node  is randomly set in the interval $[500;700]$.  A sensor node  will not participate in the  next round if its  remaining energy is less than  $E_{R}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  active state (9.72 mW) by the time in second  for one round (3600 seconds). According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.
 
 \subsection{Metrics}
 %The initial energy of each node  is randomly set in the interval $[500;700]$.  A sensor node  will not participate in the  next round if its  remaining energy is less than  $E_{R}=36~\mbox{Joules}$, the minimum  energy needed for the  node to stay alive  during one round.  This value has  been computed by  multiplying the energy consumed in  active state (9.72 mW) by the time in second  for one round (3600 seconds). According to the  interval of initial energy, a sensor may be alive during at most 20 rounds.
 
 \subsection{Metrics}

-\label{ch5:sec:03:02}
+\label{ch5:sec:04:02}

 To evaluate our approach we consider the following performance metrics:
 
 \begin{enumerate}[i]
 To evaluate our approach we consider the following performance metrics:
 
 \begin{enumerate}[i]


@@ -365,7 +403,7 @@ indicate the energy consumed by the whole network in round $t$.
 
 
 \subsection{Results Analysis and Comparison }
 
 
 \subsection{Results Analysis and Comparison }

-\label{ch5:sec:03:02}
+\label{ch5:sec:04:02}

 
 
 \begin{enumerate}[(i)]
 
 
 \begin{enumerate}[(i)]


@@ -380,18 +418,18 @@ which is a little bit better than the one of MuDiLCO.
 
 This is due  to the fact that, in comparison with  MuDiLCO which uses optimization
 to put in  SLEEP status redundant sensors, more sensor  nodes remain active with
 
 This is due  to the fact that, in comparison with  MuDiLCO which uses optimization
 to put in  SLEEP status redundant sensors, more sensor  nodes remain active with

-DESK and GAF.   As a consequence, when the number of  rounds increases, a larger
+DESK and GAF. As a consequence, when the number of  rounds increases, a larger

 number of node failures  can be observed in DESK and GAF,  resulting in a faster
 decrease of the coverage ratio.   Furthermore, our protocol allows to maintain a
 coverage ratio  greater than  50\% for far  more rounds.  Overall,  the proposed
 sensor  activity scheduling based  on optimization  in MuDiLCO  maintains higher
 coverage ratios of the  area of interest for a larger number  of rounds. It also
 number of node failures  can be observed in DESK and GAF,  resulting in a faster
 decrease of the coverage ratio.   Furthermore, our protocol allows to maintain a
 coverage ratio  greater than  50\% for far  more rounds.  Overall,  the proposed
 sensor  activity scheduling based  on optimization  in MuDiLCO  maintains higher
 coverage ratios of the  area of interest for a larger number  of rounds. It also

-means that MuDiLCO saves more energy,  with less dead nodes, at most for several
+means that MuDiLCO saves more energy,  with fewer dead nodes, at most for several

 rounds, and thus should extend the network lifetime.
 
 \begin{figure}[ht!]
 \centering
 rounds, and thus should extend the network lifetime.
 
 \begin{figure}[ht!]
 \centering

- \includegraphics[scale=0.6] {Figures/ch5/R1/CR.pdf}   
+ \includegraphics[scale=0.8] {Figures/ch5/R1/CR.pdf}   

 \caption{Average coverage ratio for 150 deployed nodes}
 \label{fig3}
 \end{figure} 
 \caption{Average coverage ratio for 150 deployed nodes}
 \label{fig3}
 \end{figure} 


@@ -409,13 +447,11 @@ and GAF have  respectively 37.6\% and 44.8\% of nodes  in ACTIVE status, whereas
 MuDiLCO clearly  outperforms them  with only 24.8\%  of active nodes.  After the
 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
 with  the  dual  observation  of  higher  level  of  coverage  made  previously.
 MuDiLCO clearly  outperforms them  with only 24.8\%  of active nodes.  After the
 thirty-fifth round, MuDiLCO exhibits larger numbers of active nodes, which agrees
 with  the  dual  observation  of  higher  level  of  coverage  made  previously.

-Obviously, in  that case DESK  and GAF have  less active nodes, since  they have
-activated many nodes  at the beginning. Anyway, MuDiLCO  activates the available
-nodes in a more efficient manner.
+Obviously, in  that case, DESK and GAF have fewer active nodes since they have activated many nodes  in the beginning. Anyway, MuDiLCO  activates the available nodes in a more efficient manner.

 
 \begin{figure}[ht!]
 \centering
 
 \begin{figure}[ht!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch5/R1/ASR.pdf}  
+\includegraphics[scale=0.8]{Figures/ch5/R1/ASR.pdf}  

 \caption{Active sensors ratio for 150 deployed nodes}
 \label{fig4}
 \end{figure} 
 \caption{Active sensors ratio for 150 deployed nodes}
 \label{fig4}
 \end{figure} 


@@ -436,7 +472,7 @@ still connected.
 
 \begin{figure}[ht!]
 \centering
 
 \begin{figure}[ht!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch5/R1/SR.pdf} 
+\includegraphics[scale=0.8]{Figures/ch5/R1/SR.pdf} 

 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
 \label{fig6}
 \end{figure} 
 \caption{Cumulative percentage of stopped simulation runs for 150 deployed nodes }
 \label{fig6}
 \end{figure} 


@@ -458,9 +494,9 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
 \centering
  %\begin{multicols}{1}
 \centering
 \centering
  %\begin{multicols}{1}
 \centering

-\includegraphics[scale=0.6]{Figures/ch5/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\
+\includegraphics[scale=0.8]{Figures/ch5/R1/EC95.pdf}\\~ ~ ~ ~ ~(a) \\

 %\vfill
 %\vfill

-\includegraphics[scale=0.6]{Figures/ch5/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)
+\includegraphics[scale=0.8]{Figures/ch5/R1/EC50.pdf}\\~ ~ ~ ~ ~(b)

 
 %\end{multicols} 
 \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
 
 %\end{multicols} 
 \caption{Energy consumption for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}


@@ -468,16 +504,8 @@ network sizes, for $Lifetime_{95}$ and $Lifetime_{50}$.
 \end{figure}
 
 
 \end{figure}
 
 

-The  results  show  that  MuDiLCO  is  the  most  competitive  from  the  energy
-consumption point of view.  The  other approaches have a high energy consumption
-due  to activating a  larger number  of redundant  nodes as  well as  the energy
-consumed during  the different  status of the  sensor node. Among  the different
-versions of our protocol, the MuDiLCO-7  one consumes more energy than the other
-versions. This is  easy to understand since the bigger the  number of rounds and
-the number of  sensors involved in the integer program are,  the larger the time
-computation to solve the optimization problem is. To improve the performances of
-MuDiLCO-7, we  should increase the  number of subregions  in order to  have less
-sensors to consider in the integer program.
+The  results  show  that  MuDiLCO  is  the  most  competitive  from  the  energy consumption point of view.  The  other approaches have a high energy consumption due  to activating a  larger number  of redundant  nodes, as  well as  the energy consumed during  the different  status of the  sensor node. Among  the different versions of our protocol, the MuDiLCO-7  one consumes more energy than the other versions. This is  easy to understand since the bigger the  number of rounds and
+the number of  sensors involved in the integer program is  the larger the time computation to solve the optimization problem is. To improve the performances of MuDiLCO-7, we  should increase the  number of subregions  in order to  have fewer sensors to consider in the integer program.

 
 
 
 
 
 


@@ -493,21 +521,13 @@ seconds (needed to solve optimization problem) for different values of $T$. The
 
 \begin{figure}[ht!]
 \centering
 
 \begin{figure}[ht!]
 \centering

-\includegraphics[scale=0.6]{Figures/ch5/R1/T.pdf}  
+\includegraphics[scale=0.8]{Figures/ch5/R1/T.pdf}  

 \caption{Execution Time (in seconds)}
 \label{fig77}
 \end{figure} 
 
 \caption{Execution Time (in seconds)}
 \label{fig77}
 \end{figure} 
 

-As expected,  the execution time increases  with the number of  rounds $T$ taken
-into account to schedule the sensing phase. The times obtained for $T=1,3$
-or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor
-node, especially when  the sensor network size increases.   Again, we can notice
-that if we want  to schedule the nodes activities for a  large number of rounds,
-we need to choose a relevant number of subregions in order to avoid a complicated
-and cumbersome optimization.  On the one hand, a large value  for $T$ permits to
-reduce the  energy-overhead due  to the three  pre-sensing phases, on  the other
-hand  a leader  node may  waste a  considerable amount  of energy  to  solve the
-optimization problem.
+As expected,  the execution time increases  with the number of  rounds $T$ taken into account to schedule the sensing phase. The times obtained for $T=1,3$ or $5$ seem bearable, but for $T=7$ they become quickly unsuitable for a sensor node, especially when  the sensor network size increases.   Again, we can notice that if we want  to schedule the nodes activities for a  large number of rounds,
+we need to choose a relevant number of subregions in order to avoid a complicated and cumbersome optimization.  On the one hand, a large value  for $T$ permits to reduce the  energy overhead due  to the three  pre-sensing phases, on  the other hand  a leader  node may  waste a  considerable amount  of energy  to  solve the optimization problem.

 
 
 
 
 
 


@@ -515,29 +535,19 @@ optimization problem.
 %\subsection{Network lifetime}
 %\label{ch5:sec:03:02:06}
 
 %\subsection{Network lifetime}
 %\label{ch5:sec:03:02:06}
 

-The next  two figures,  Figures~\ref{fig8}(a) and \ref{fig8}(b),  illustrate the
-network lifetime  for different network sizes,  respectively for $Lifetime_{95}$
-and  $Lifetime_{50}$.  Both  figures show  that the  network  lifetime increases
-together with the  number of sensor nodes, whatever the  protocol, thanks to the
-node  density  which  results in  more  and  more  redundant  nodes that  can  be
-deactivated and thus save energy.  Compared to the other approaches, our MuDiLCO
-protocol  maximizes the  lifetime of  the network.   In particular  the  gain in
-lifetime for a  coverage over 95\% is greater than 38\%  when switching from GAF
-to MuDiLCO-3.  The  slight decrease that can be observed  for MuDiLCO-7 in case
-of  $Lifetime_{95}$  with  large  wireless  sensor  networks  results  from  the
-difficulty  of the optimization  problem to  be solved  by the  integer program.
+The next  two figures,  Figures~\ref{fig8}(a) and \ref{fig8}(b),  illustrate the network lifetime  for different network sizes,  respectively for $Lifetime_{95}$ and  $Lifetime_{50}$.  Both  figures show  that the  network  lifetime increases together with the  number of sensor nodes, whatever the  protocol, thanks to the node  density  which  results in  more  and  more  redundant  nodes that  can  be deactivated and thus save energy.  Compared to the other approaches, our MuDiLCO
+protocol  maximizes the  lifetime of  the network.   In particular,  the  gain in lifetime for a  coverage over 95\% is greater than 38\%  when switching from GAF to MuDiLCO-3.  The  slight decrease that can be observed  for MuDiLCO-7 in case of  $Lifetime_{95}$  with  large  wireless  sensor  networks  results  from  the difficulty  of the optimization  problem to  be solved  by the  integer program.

 This  point was  already noticed  in \ref{subsec:EC} devoted  to the
 This  point was  already noticed  in \ref{subsec:EC} devoted  to the

-energy consumption,  since network lifetime and energy  consumption are directly
-linked.
+energy consumption,  since network lifetime and energy  consumption are directly linked.

 
 
 \begin{figure}[h!]
 \centering
 % \begin{multicols}{0}
 \centering
 
 
 \begin{figure}[h!]
 \centering
 % \begin{multicols}{0}
 \centering

-\includegraphics[scale=0.6]{Figures/ch5/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\
+\includegraphics[scale=0.8]{Figures/ch5/R1/LT95.pdf}\\~ ~ ~ ~ ~(a) \\

 %\hfill 
 %\hfill 

-\includegraphics[scale=0.6]{Figures/ch5/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)
+\includegraphics[scale=0.8]{Figures/ch5/R1/LT50.pdf}\\~ ~ ~ ~ ~(b)

 
 %\end{multicols} 
 \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}
 
 %\end{multicols} 
 \caption{Network lifetime for (a) $Lifetime_{95}$ and (b) $Lifetime_{50}$}


@@ -550,32 +560,14 @@ linked.
 
 
 \section{Conclusion}
 
 
 \section{Conclusion}

-\label{ch5:sec:04}
+\label{ch5:sec:05}
+
+We have addressed  the problem of the coverage and of the lifetime optimization in wireless  sensor networks.  This is  a key  issue as  sensor nodes  have limited resources in terms of memory, energy, and computational power. To cope with this problem,  the field  of sensing  is divided  into smaller  subregions  using the concept  of divide-and-conquer  method, and  then  we propose  a protocol  which optimizes coverage  and lifetime performances in each  subregion.  Our protocol,
+called MuDiLCO (Multiround  Distributed Lifetime Coverage Optimization) combines two  efficient   techniques:  network   leader  election  and   sensor  activity scheduling.
+
+The activity  scheduling in each subregion  works in periods,  where each period consists of four  phases: (i) Information Exchange, (ii)  Leader Election, (iii) Decision Phase to plan the activity  of the sensors over $T$ rounds, (iv) Sensing Phase itself divided into T rounds.

 
 

-We have addressed  the problem of the coverage and of the lifetime optimization in
-wireless  sensor networks.  This is  a key  issue as  sensor nodes  have limited
-resources in terms of memory, energy, and computational power. To cope with this
-problem,  the field  of sensing  is divided  into smaller  subregions  using the
-concept  of divide-and-conquer  method, and  then  we propose  a protocol  which
-optimizes coverage  and lifetime performances in each  subregion.  Our protocol,
-called MuDiLCO (Multiround  Distributed Lifetime Coverage Optimization) combines
-two  efficient   techniques:  network   leader  election  and   sensor  activity
-scheduling.
-
-The activity  scheduling in each subregion  works in periods,  where each period
-consists of four  phases: (i) Information Exchange, (ii)  Leader Election, (iii)
-Decision Phase to plan the activity  of the sensors over $T$ rounds, (iv) Sensing
-Phase itself divided into T rounds.
-
-Simulations  results show the  relevance of  the proposed  protocol in  terms of
-lifetime, coverage  ratio, active  sensors ratio, energy  consumption, execution
-time. Indeed,  when dealing with  large wireless sensor networks,  a distributed
-approach, like  the one we  propose, allows to  reduce the difficulty of  a single
-global optimization problem by partitioning it in many smaller problems, one per
-subregion, that can be solved  more easily. Nevertheless, results also show that
-it is not possible to plan the activity of sensors over too many rounds, because
-the resulting optimization problem leads to too high resolution times and thus to
-an excessive energy consumption.
+Simulations  results show the  relevance of  the proposed  protocol in  terms of lifetime, coverage  ratio, active  sensors ratio, energy  consumption, execution time. Indeed,  when dealing with  large wireless sensor networks,  a distributed approach, like  the one we  propose, allows to  reduce the difficulty of  a single global optimization problem by partitioning it into many smaller problems, one per subregion, that can be solved  more easily. Nevertheless, results also show that it is not possible to plan the activity of sensors over too many rounds because the resulting optimization problem leads to too high-resolution times and thus to an excessive energy consumption.